triangleFuncs.C

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/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Copyright (C) 2011-2022 OpenFOAM Foundation
     \\/     M anipulation  |
-------------------------------------------------------------------------------
License
    This file is part of OpenFOAM.
 
    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    for more details.
 
    You should have received a copy of the GNU General Public License
    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
\*---------------------------------------------------------------------------*/
 
#include "triangleFuncs.H"
#include "pointField.H"
#include "treeBoundBox.H"
#include "SortableList.H"
#include "boolList.H"
 
// * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
void Foam::triangleFuncs::setIntersection
(
    const point& oppositeSidePt,
    const scalar oppositeSign,
 
    const point& thisSidePt,
    const scalar thisSign,
 
    const scalar tol,
 
    point& pt
)
{
    scalar denom = oppositeSign - thisSign;
 
    if (mag(denom) < tol)
    {
        // If almost does not cut choose one which certainly cuts.
        pt = oppositeSidePt;
    }
    else
    {
        pt = oppositeSidePt + oppositeSign/denom*(thisSidePt - oppositeSidePt);
    }
}
 
 
void Foam::triangleFuncs::selectPt
(
    const bool select0,
    const point& p0,
    const point& p1,
    point& min
)
{
    if (select0)
    {
        min = p0;
    }
    else
    {
        min = p1;
    }
}
 
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
// Intersect triangle with parallel edges aligned with axis i0.
// Returns true (and intersection in pInter) if any of them intersects triangle.
bool Foam::triangleFuncs::intersectAxesBundle
(
    const point& V0,
    const point& V10,
    const point& V20,
    const label i0,
    const pointField& origin,
    const scalar maxLength,
    point& pInter
)
{
    // Based on Graphics Gems - Fast Ray Triangle intersection.
    // Since direction is coordinate axis there is no need to do projection,
    // we can directly check u,v components for inclusion in triangle.
 
    // Get other components
    const label i1 = (i0 + 1) % 3;
    const label i2 = (i1 + 1) % 3;
 
    const scalar u1 = V10[i1];
    const scalar v1 = V10[i2];
 
    const scalar u2 = V20[i1];
    const scalar v2 = V20[i2];
 
    const scalar localScale = mag(u1) + mag(v1) + mag(u2) + mag(v2);
 
    const scalar det = v2*u1 - u2*v1;
 
    // Fix for  V0:(-31.71428 0 -15.10714)
    //          V10:(-1.285715 8.99165e-16 -1.142858)
    //          V20:(0 0 -1.678573)
    //          i0:0
    if (localScale < vSmall || Foam::mag(det)/localScale < small)
    {
        // Triangle parallel to dir
        return false;
    }
 
    forAll(origin, originI)
    {
        const point& P = origin[originI];
 
        const scalar u0 = P[i1] - V0[i1];
        const scalar v0 = P[i2] - V0[i2];
 
        scalar alpha = 0;
        scalar beta = 0;
        bool inter = false;
 
        if (mag(u1) < rootVSmall)
        {
            beta = u0/u2;
            if ((beta >= 0) && (beta <= 1))
            {
                alpha = (v0 - beta*v2)/v1;
                inter = ((alpha >= 0) && ((alpha + beta) <= 1));
            }
        }
        else
        {
            beta = (v0*u1 - u0*v1)/det;
            if ((beta >= 0) && (beta <= 1))
            {
                alpha = (u0 - beta*u2)/u1;
                inter = ((alpha >= 0) && ((alpha + beta) <= 1));
            }
        }
 
        if (inter)
        {
            pInter = V0 + alpha*V10 + beta*V20;
            const scalar s = pInter[i0] - P[i0];
 
            if ((s >= 0) && (s <= maxLength))
            {
                return true;
            }
        }
    }
 
    return false;
}
 
 
// Intersect triangle with bounding box. Return true if
// any of the faces of bb intersect triangle.
// Note: so returns false if triangle inside bb.
bool Foam::triangleFuncs::intersectBb
(
    const point& p0,
    const point& p1,
    const point& p2,
    const treeBoundBox& cubeBb
)
{
    const vector p10 = p1 - p0;
    const vector p20 = p2 - p0;
 
    // cubeBb points; counted as if cell with vertex0 at cubeBb.min().
    const point& min = cubeBb.min();
    const point& max = cubeBb.max();
 
    const point& cube0 = min;
    const point  cube1(min.x(), min.y(), max.z());
    const point  cube2(max.x(), min.y(), max.z());
    const point  cube3(max.x(), min.y(), min.z());
 
    const point  cube4(min.x(), max.y(), min.z());
    const point  cube5(min.x(), max.y(), max.z());
    const point  cube7(max.x(), max.y(), min.z());
 
    //
    // Intersect all 12 edges of cube with triangle
    //
 
    point pInter;
    pointField origin(4);
    // edges in x direction
    origin[0] = cube0;
    origin[1] = cube1;
    origin[2] = cube5;
    origin[3] = cube4;
 
    scalar maxSx = max.x() - min.x();
 
    if (intersectAxesBundle(p0, p10, p20, 0, origin, maxSx, pInter))
    {
        return true;
    }
 
    // edges in y direction
    origin[0] = cube0;
    origin[1] = cube1;
    origin[2] = cube2;
    origin[3] = cube3;
 
    scalar maxSy = max.y() - min.y();
 
    if (intersectAxesBundle(p0, p10, p20, 1, origin, maxSy, pInter))
    {
        return true;
    }
 
    // edges in z direction
    origin[0] = cube0;
    origin[1] = cube3;
    origin[2] = cube7;
    origin[3] = cube4;
 
    scalar maxSz = max.z() - min.z();
 
    if (intersectAxesBundle(p0, p10, p20, 2, origin, maxSz, pInter))
    {
        return true;
    }
 
 
    // Intersect triangle edges with bounding box
    if (cubeBb.intersects(p0, p1, pInter))
    {
        return true;
    }
    if (cubeBb.intersects(p1, p2, pInter))
    {
        return true;
    }
    if (cubeBb.intersects(p2, p0, pInter))
    {
        return true;
    }
 
    return false;
}
 
 
//bool Foam::triangleFuncs::intersectBbExact
//(
//    const point& p0,
//    const point& p1,
//    const point& p2,
//    const treeBoundBox& cubeBb
//)
//{
//    const point& min = cubeBb.min();
//    const point& max = cubeBb.max();
//
//    const point& cube0 = min;
//    const point  cube1(min.x(), min.y(), max.z());
//    const point  cube2(max.x(), min.y(), max.z());
//    const point  cube3(max.x(), min.y(), min.z());
//
//    const point  cube4(min.x(), max.y(), min.z());
//    const point  cube5(min.x(), max.y(), max.z());
//    const point& cube6 = max;
//    const point  cube7(max.x(), max.y(), min.z());
//
//    // Test intersection of triangle with twelve edges of box.
//    {
//        triPointRef tri(p0, p1, p2);
//        if (tri.intersectionExact(cube0, cube1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(cube1, cube2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(cube2, cube3).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(cube3, cube0).hit())
//        {
//            return true;
//        }
//
//        if (tri.intersectionExact(cube4, cube5).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(cube5, cube6).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(cube6, cube7).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(cube7, cube4).hit())
//        {
//            return true;
//        }
//
//        if (tri.intersectionExact(cube0, cube4).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(cube1, cube5).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(cube2, cube6).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(cube3, cube7).hit())
//        {
//            return true;
//        }
//    }
//    // Test intersection of triangle edges with bounding box
//    {
//        triPointRef tri(cube0, cube1, cube2);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//    {
//        triPointRef tri(cube2, cube3, cube0);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//    {
//        triPointRef tri(cube4, cube5, cube6);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//    {
//        triPointRef tri(cube6, cube7, cube4);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//
//
//    {
//        triPointRef tri(cube4, cube5, cube1);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//    {
//        triPointRef tri(cube1, cube0, cube4);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//    {
//        triPointRef tri(cube7, cube6, cube2);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//    {
//        triPointRef tri(cube2, cube3, cube7);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//
//    {
//        triPointRef tri(cube0, cube4, cube7);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//    {
//        triPointRef tri(cube7, cube3, cube0);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//    {
//        triPointRef tri(cube1, cube5, cube6);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//    {
//        triPointRef tri(cube6, cube2, cube1);
//        if (tri.intersectionExact(p0, p1).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p1, p2).hit())
//        {
//            return true;
//        }
//        if (tri.intersectionExact(p2, p0).hit())
//        {
//            return true;
//        }
//    }
//    return false;
//}
 
 
bool Foam::triangleFuncs::intersect
(
    const point& va0,
    const point& va10,
    const point& va20,
 
    const point& base,
    const point& normal,
 
    point& pInter0,
    point& pInter1
)
{
    // Get triangle normal
    vector na = va10 ^ va20;
    scalar magArea = mag(na);
    na/magArea;
 
    if (mag(na & normal) > (1 - small))
    {
        // Parallel
        return false;
    }
 
    const point va1 = va0 + va10;
    const point va2 = va0 + va20;
 
    // Find the triangle point on the other side.
    scalar sign0 = (va0 - base) & normal;
    scalar sign1 = (va1 - base) & normal;
    scalar sign2 = (va2 - base) & normal;
 
    label oppositeVertex = -1;
 
    if (sign0 < 0)
    {
        if (sign1 < 0)
        {
            if (sign2 < 0)
            {
                // All on same side of plane
                return false;
            }
            else    // sign2 >= 0
            {
                // 2 on opposite side.
                oppositeVertex = 2;
            }
        }
        else    // sign1 >= 0
        {
            if (sign2 < 0)
            {
                // 1 on opposite side.
                oppositeVertex = 1;
            }
            else
            {
                // 0 on opposite side.
                oppositeVertex = 0;
            }
        }
    }
    else    // sign0 >= 0
    {
        if (sign1 < 0)
        {
            if (sign2 < 0)
            {
                // 0 on opposite side.
                oppositeVertex = 0;
            }
            else    // sign2 >= 0
            {
                // 1 on opposite side.
                oppositeVertex = 1;
            }
        }
        else    // sign1 >= 0
        {
            if (sign2 < 0)
            {
                // 2 on opposite side.
                oppositeVertex = 2;
            }
            else    // sign2 >= 0
            {
                // All on same side of plane
                return false;
            }
        }
    }
 
    scalar tol = small*Foam::sqrt(magArea);
 
    if (oppositeVertex == 0)
    {
        // 0 on opposite side. Cut edges 01 and 02
        setIntersection(va0, sign0, va1, sign1, tol, pInter0);
        setIntersection(va0, sign0, va2, sign2, tol, pInter1);
    }
    else if (oppositeVertex == 1)
    {
        // 1 on opposite side. Cut edges 10 and 12
        setIntersection(va1, sign1, va0, sign0, tol, pInter0);
        setIntersection(va1, sign1, va2, sign2, tol, pInter1);
    }
    else // oppositeVertex == 2
    {
        // 2 on opposite side. Cut edges 20 and 21
        setIntersection(va2, sign2, va0, sign0, tol, pInter0);
        setIntersection(va2, sign2, va1, sign1, tol, pInter1);
    }
 
    return true;
}
 
 
bool Foam::triangleFuncs::intersect
(
    const point& va0,
    const point& va10,
    const point& va20,
 
    const point& vb0,
    const point& vb10,
    const point& vb20,
 
    point& pInter0,
    point& pInter1
)
{
    // Get triangle normals
    vector na = va10 ^ va20;
    na/mag(na);
 
    vector nb = vb10 ^ vb20;
    nb/mag(nb);
 
    // Calculate intersection of triangle a with plane of b
    point planeB0;
    point planeB1;
    if (!intersect(va0, va10, va20, vb0, nb, planeB0, planeB1))
    {
        return false;
    }
 
    //       ,,  triangle b with plane of a
    point planeA0;
    point planeA1;
    if (!intersect(vb0, vb10, vb20, va0, na, planeA0, planeA1))
    {
        return false;
    }
 
    // Now check if intersections overlap (w.r.t. intersection of the two
    // planes)
 
    vector intersection(na ^ nb);
 
    scalar coordB0 = planeB0 & intersection;
    scalar coordB1 = planeB1 & intersection;
 
    scalar coordA0 = planeA0 & intersection;
    scalar coordA1 = planeA1 & intersection;
 
    // Put information in indexable form for sorting.
    List<point*> pts(4);
    boolList isFromB(4);
    SortableList<scalar> sortCoords(4);
 
    pts[0] = &planeB0;
    isFromB[0] = true;
    sortCoords[0] = coordB0;
 
    pts[1] = &planeB1;
    isFromB[1] = true;
    sortCoords[1] = coordB1;
 
    pts[2] = &planeA0;
    isFromB[2] = false;
    sortCoords[2] = coordA0;
 
    pts[3] = &planeA1;
    isFromB[3] = false;
    sortCoords[3] = coordA1;
 
    sortCoords.sort();
 
    const labelList& indices = sortCoords.indices();
 
    if (isFromB[indices[0]] == isFromB[indices[1]])
    {
        // Entry 0 and 1 are of same region (both a or both b). Hence that
        // region does not overlap.
        return false;
    }
    else
    {
        // Different type. Start of overlap at indices[1], end at indices[2]
        pInter0 = *pts[indices[1]];
        pInter1 = *pts[indices[2]];
 
        return true;
    }
}
 
 
// ************************************************************************* //